Question: Solve for $x$ and $y$ using elimination. ${-2x+2y = 6}$ ${-5x-2y = -34}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $-7x = -28$ $\dfrac{-7x}{{-7}} = \dfrac{-28}{{-7}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-2x+2y = 6}\thinspace$ to find $y$ ${-2}{(4)}{ + 2y = 6}$ $-8+2y = 6$ $-8{+8} + 2y = 6{+8}$ $2y = 14$ $\dfrac{2y}{{2}} = \dfrac{14}{{2}}$ ${y = 7}$ You can also plug ${x = 4}$ into $\thinspace {-5x-2y = -34}\thinspace$ and get the same answer for $y$ : ${-5}{(4)}{ - 2y = -34}$ ${y = 7}$